Well every flight booking I've made with KLM has been in some version of Firefox, so it doesn't make sense that it works sometimes and other times it doesn't.

The report broken website application in Firefox is only really useful for things that are either the fault of the browser or are easily reproducable. Basically if the bug is with the website then it's up to Mozilla volunteers to contact the authors of broken websites. It's a thankless job so I can imagine it's only major sites that get bothered with.

Here's a list of reports from this tool for klm.com:
http://reporter.mozilla.org/app/quer...t_query=Search